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Title:
Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture
Authors:
Lu, Peter J.; Steinhardt, Paul J.
Affiliation:
AA(Department of Physics, Harvard University, Cambridge, MA 02138, USA.), AB(Department of Physics and Princeton Center for Theoretical Physics, Princeton University, Princeton, NJ 08544, USA.)
Publication:
Science, Volume 315, Issue 5815, pp. 1106- (2007). (Sci Homepage)
Publication Date:
02/2007
Category:
COMP/MATH
Origin:
SCIENCE
Abstract Copyright:
(c) 2007: Science
DOI:
10.1126/science.1135491
Bibliographic Code:
2007Sci...315.1106L

Abstract

The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (``girih tiles'') decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.
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Database: Astronomy
Physics
arXiv e-prints